A silver dollar is flipped twice. Calculate the probability of each of the following occurring: a head on the first flip a tail on the second flip given that the first toss was a head two tails a tail on the first and a head on the second a tail on the first and a head on the second or a head on the first and a tail on the second at least one head on the two flips

Explained below.

Step-by-step explanation:

The sample space for flipping a dollar twice is:

S = {HH, HT, TH, TT}

n (S) = 4

Independent events are those events that does not affect each other.

In this case, the outcomes of the two tosses are independent, i.e. the outcome of the second toss does not depends on the second toss.

(1)

Compute the probability of a head on the first flip:

The favorable outcomes are:

H₁ = {HH, HT}

n (H₁) = 2

(2)

Compute the probability of a tail on the second flip given that the first toss was a head:

The favorable outcomes are:

T₂ | H₁ = {HT}

n (T₂ | H₁) = 1

(3)

Compute the probability of two tails:

T₁ and T₂ = {TT}

n (T₁ and T₂) = 1

(4)

Compute the probability of a tail on the first and a head on the second:

T₁ and H₂ = {TH}

n (T₁ and H₂) = 1

(5)

Compute the probability of at least one head on the two flips:

s = {HH, HT, TH}

n (s) = 3

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841